TSTP Solution File: RNG095+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG095+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:57:50 EDT 2023
% Result : Theorem 21.70s 3.70s
% Output : Proof 22.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG095+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 02:37:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.85/1.10 Prover 4: Preprocessing ...
% 2.85/1.10 Prover 1: Preprocessing ...
% 2.85/1.14 Prover 6: Preprocessing ...
% 2.85/1.14 Prover 3: Preprocessing ...
% 2.85/1.14 Prover 0: Preprocessing ...
% 2.85/1.14 Prover 2: Preprocessing ...
% 2.85/1.14 Prover 5: Preprocessing ...
% 7.00/1.72 Prover 1: Constructing countermodel ...
% 7.63/1.76 Prover 3: Constructing countermodel ...
% 7.63/1.78 Prover 6: Proving ...
% 8.14/1.85 Prover 5: Proving ...
% 8.14/1.85 Prover 2: Proving ...
% 8.14/1.87 Prover 4: Constructing countermodel ...
% 8.47/1.91 Prover 0: Proving ...
% 15.35/2.78 Prover 3: gave up
% 15.35/2.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.35/2.85 Prover 7: Preprocessing ...
% 16.46/2.99 Prover 7: Constructing countermodel ...
% 21.70/3.69 Prover 7: Found proof (size 17)
% 21.70/3.70 Prover 7: proved (898ms)
% 21.70/3.70 Prover 0: stopped
% 21.70/3.70 Prover 6: stopped
% 21.70/3.70 Prover 2: stopped
% 21.70/3.70 Prover 1: stopped
% 21.70/3.70 Prover 5: stopped
% 21.70/3.70 Prover 4: stopped
% 21.70/3.70
% 21.70/3.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.70/3.70
% 21.70/3.70 % SZS output start Proof for theBenchmark
% 21.70/3.71 Assumptions after simplification:
% 21.70/3.71 ---------------------------------
% 21.70/3.71
% 21.70/3.71 (mDefIdeal)
% 22.21/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1)
% 22.21/3.74 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~
% 22.21/3.74 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i]
% 22.21/3.74 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~
% 22.21/3.74 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) |
% 22.21/3.74 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 22.21/3.74 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) |
% 22.21/3.74 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ?
% 22.21/3.74 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2,
% 22.21/3.74 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) |
% 22.21/3.74 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~
% 22.21/3.74 aElementOf0(v5, v0)))))
% 22.21/3.74
% 22.21/3.74 (mDefSSum)
% 22.21/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 22.21/3.74 $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ $i(v5) |
% 22.21/3.74 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 22.21/3.74 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) |
% 22.21/3.74 aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 22.21/3.74 : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 22.21/3.75 ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ? [v5: $i] : ?
% 22.21/3.75 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3)
% 22.21/3.75 | ! [v8: $i] : ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ $i(v9) |
% 22.21/3.75 ~ $i(v8) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) &
% 22.21/3.75 (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6,
% 22.21/3.75 v1) & aElementOf0(v5, v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 22.21/3.75 $i] : ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 22.21/3.75 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) |
% 22.21/3.75 ? [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 22.21/3.75 aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0: $i] : ! [v1: $i] :
% 22.21/3.75 ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 22.21/3.75 ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2))
% 22.21/3.75
% 22.21/3.75 (mSortsC_01)
% 22.21/3.75 $i(sz10) & aElement0(sz10)
% 22.21/3.75
% 22.21/3.75 (m__)
% 22.21/3.75 $i(xJ) & $i(xI) & $i(sz10) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, v1)
% 22.21/3.75 = sz10) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | ~
% 22.21/3.75 aElementOf0(v0, xI))
% 22.21/3.75
% 22.21/3.75 (m__1205)
% 22.21/3.75 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI)
% 22.21/3.75
% 22.21/3.75 (m__1205_03)
% 22.21/3.75 $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & ! [v1: $i]
% 22.21/3.75 : ( ~ $i(v1) | ~ aElement0(v1) | aElementOf0(v1, v0)))
% 22.21/3.75
% 22.21/3.75 Further assumptions not needed in the proof:
% 22.21/3.75 --------------------------------------------
% 22.21/3.75 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefMod, mDefSInt,
% 22.21/3.75 mEOfElem, mElmSort, mIdeInt, mIdeSum, mMulAsso, mMulComm, mMulMnOne, mMulUnit,
% 22.21/3.75 mMulZero, mSetEq, mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsU, mUnNeZr,
% 22.21/3.75 m__1217
% 22.21/3.75
% 22.21/3.75 Those formulas are unsatisfiable:
% 22.21/3.75 ---------------------------------
% 22.21/3.75
% 22.21/3.75 Begin of proof
% 22.21/3.75 |
% 22.21/3.75 | ALPHA: (mSortsC_01) implies:
% 22.21/3.75 | (1) aElement0(sz10)
% 22.21/3.75 |
% 22.21/3.75 | ALPHA: (mDefSSum) implies:
% 22.21/3.75 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 22.21/3.75 | (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 22.21/3.75 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | ?
% 22.21/3.75 | [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 22.21/3.75 | aElementOf0(v5, v1) & aElementOf0(v4, v0)))
% 22.21/3.75 |
% 22.21/3.75 | ALPHA: (mDefIdeal) implies:
% 22.21/3.75 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ aIdeal0(v0) | aSet0(v0))
% 22.21/3.75 |
% 22.21/3.75 | ALPHA: (m__1205) implies:
% 22.21/3.76 | (4) aIdeal0(xI)
% 22.21/3.76 | (5) aIdeal0(xJ)
% 22.21/3.76 |
% 22.21/3.76 | ALPHA: (m__1205_03) implies:
% 22.21/3.76 | (6) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 22.21/3.76 | $i(v1) | ~ aElement0(v1) | aElementOf0(v1, v0)))
% 22.21/3.76 |
% 22.21/3.76 | ALPHA: (m__) implies:
% 22.21/3.76 | (7) $i(sz10)
% 22.21/3.76 | (8) $i(xI)
% 22.21/3.76 | (9) $i(xJ)
% 22.21/3.76 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, v1) = sz10) | ~ $i(v1)
% 22.21/3.76 | | ~ $i(v0) | ~ aElementOf0(v1, xJ) | ~ aElementOf0(v0, xI))
% 22.21/3.76 |
% 22.21/3.76 | DELTA: instantiating (6) with fresh symbol all_26_0 gives:
% 22.21/3.76 | (11) sdtpldt1(xI, xJ) = all_26_0 & $i(all_26_0) & ! [v0: $i] : ( ~ $i(v0)
% 22.21/3.76 | | ~ aElement0(v0) | aElementOf0(v0, all_26_0))
% 22.21/3.76 |
% 22.21/3.76 | ALPHA: (11) implies:
% 22.21/3.76 | (12) $i(all_26_0)
% 22.21/3.76 | (13) sdtpldt1(xI, xJ) = all_26_0
% 22.21/3.76 | (14) ! [v0: $i] : ( ~ $i(v0) | ~ aElement0(v0) | aElementOf0(v0,
% 22.21/3.76 | all_26_0))
% 22.21/3.76 |
% 22.21/3.76 | GROUND_INST: instantiating (14) with sz10, simplifying with (1), (7) gives:
% 22.21/3.76 | (15) aElementOf0(sz10, all_26_0)
% 22.21/3.76 |
% 22.21/3.76 | GROUND_INST: instantiating (3) with xI, simplifying with (4), (8) gives:
% 22.21/3.76 | (16) aSet0(xI)
% 22.21/3.76 |
% 22.21/3.76 | GROUND_INST: instantiating (3) with xJ, simplifying with (5), (9) gives:
% 22.21/3.76 | (17) aSet0(xJ)
% 22.21/3.76 |
% 22.21/3.76 | GROUND_INST: instantiating (2) with xI, xJ, all_26_0, sz10, simplifying with
% 22.21/3.76 | (7), (8), (9), (12), (13), (15), (16), (17) gives:
% 22.21/3.76 | (18) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, v1) = sz10 & $i(v1) & $i(v0)
% 22.21/3.76 | & aElementOf0(v1, xJ) & aElementOf0(v0, xI))
% 22.21/3.76 |
% 22.21/3.76 | DELTA: instantiating (18) with fresh symbols all_52_0, all_52_1 gives:
% 22.21/3.76 | (19) sdtpldt0(all_52_1, all_52_0) = sz10 & $i(all_52_0) & $i(all_52_1) &
% 22.21/3.76 | aElementOf0(all_52_0, xJ) & aElementOf0(all_52_1, xI)
% 22.21/3.76 |
% 22.21/3.76 | ALPHA: (19) implies:
% 22.21/3.76 | (20) aElementOf0(all_52_1, xI)
% 22.21/3.76 | (21) aElementOf0(all_52_0, xJ)
% 22.21/3.76 | (22) $i(all_52_1)
% 22.21/3.76 | (23) $i(all_52_0)
% 22.21/3.76 | (24) sdtpldt0(all_52_1, all_52_0) = sz10
% 22.21/3.76 |
% 22.21/3.76 | GROUND_INST: instantiating (10) with all_52_1, all_52_0, simplifying with
% 22.21/3.76 | (20), (21), (22), (23), (24) gives:
% 22.21/3.76 | (25) $false
% 22.21/3.76 |
% 22.21/3.76 | CLOSE: (25) is inconsistent.
% 22.21/3.76 |
% 22.21/3.76 End of proof
% 22.21/3.77 % SZS output end Proof for theBenchmark
% 22.21/3.77
% 22.21/3.77 3152ms
%------------------------------------------------------------------------------